Computation of generalized inverses by using the LDL∗ decomposition

AbstractAn efficient algorithm, based on the LDL∗ factorization, for computing {1,2,3} and {1,2,4} inverses and the Moore–Penrose inverse of a given rational matrix A, is developed. We consider matrix products A∗A and AA∗ and corresponding LDL∗ factorizations in order to compute the generalized inverse of A. By considering the matrix products (R∗A)†R∗ and T∗(AT∗)†, where R and T are arbitrary rational matrices with appropriate dimensions and ranks, we characterize classes A{1,2,3} and A{1,2,4}. Some evaluation times for our algorithm are compared with corresponding times for several known algorithms for computing the Moore–Penrose inverse

Optimizacija proizvodnje biodizela kukuruznog ulja metanolizom katalizovanom pepelom kurdeljke

The use of low-cost or priceless feedstocks such as byproducts in biodiesel production results in a reduced overall process costs. The present paper reports the use of corn germs and corn cobs as byproducts from corn-based starch production in the biodiesel production by the methanolysis of the oil extracted from corn germs, catalyzed by the ash produced by combustion of corn cobs. The major aim was to optimize the methanol-to-oil molar ratio, catalyst loading, and reaction time in a batch stirred reactor with respect to the content of methyl ester fatty acids (FAME). The statistical modeling and optimization were carried out using a second-order polynomial (quadratic) model developed by the response surface methodology combined with a 33 factorial design with 3 central points. The FAME content was determined by a high-pressure liquid chromatography method. The analysis of variance showed that only the catalyst amount, the reaction time, the catalyst amount interaction with reaction time and all three quadratic terms were the significant model terms with the confidence level of 95 %. The optimum reaction conditions (the catalyst amounts of 19.8 %, the methanol-to-oil molar ratio of 9.4 mol/mol and the reaction time of 31 min) provided the FAME content of 98.1 %, which was in an excellent agreement with the predicted FAME content (98.4 %). Thus, both corn germs and corn cobs may be suitable feedstocks for biodiesel production.Upotreba jeftinih ili bezvrednih sirovina, kao što su sporedni proizvodi, u proizvodnji biodizela ima za rezultat smanjene ukupne troškove procesa. U ovom radu su prikazani rezultati upotrebe kukuruznih klica i okrunjenog kukuruznog klipa (kurdeljke, krudeljke) kao sporednih proizvoda iz proizvodnje kukuruznog skroba u proizvodnji biodizela metanolizom ulja izdvojenog iz kukuruznih klica, katalizovane pepelom dobijenim sagorevanjem kurdeljke. Glavni cilj je bila optimizacija molskog odnosa metanol-ulje, količine katalizatora i reakcionog vremena u šaržnom reaktoru sa mešanjem u odnosu na sadržaj metilestra masnih kiselina (MEMK). Statističko modelovanje i optimizacija izvršeni su korišćenjem kvadratnog modela, razvijenog metodologijom odzivne površine, u kombinaciji sa 33 faktorijelnim planom sa 3 centralne tačke. Sadržaj MEMK-a je određen metodom tečne hromatografije pod visokim pritiskom. Analiza varijanse je pokazala da su samo uticaji količine katalizatora, reakcionog vremena, interakcije količine katalizatora sa reakcionim vremenom i sva tri kvadratna člana statistički značajni sa nivoom pouzdanosti od 95 %. Pod optimalnim reakcionim uslovima (količina katalizatora 19,8 %, molski odnos metanol/ulje 9,4 mol/mol i reakciono vreme 31 min) dobijen je sadržaj MEMK-a od 98,1 %, koji se slaže sa predviđenim sadržajem MEMK-a (98,4 %). Prema tome, i kukuruzne klice i kurdeljka mogu biti pogodne sirovine za proizvodnju biodizela

ANALYSIS OF PATIENTS’ NONADHERENCE TO STATIN THERAPY FROM CARDIOVASCULAR EVENT TO CARDIOVASCULAR REHABILITATION

Numerous studies have pointed to low adherence to statin, which decreases as time period from acute cardiovascular event elapses. The aim was to analyze the cause of not taking statin by patients who were referred to rehabilitation after coronary event. Study population and methods. The research included the total of 573 patients, average age 60.3, while 305 (53.1%) of them were patients who experienced the first cardiovascular event. The stated research was conducted by means of a questionnaire and implied active participation of the researchers in terms of monitoring the possession and use of medication during rehabilitation. On arrival to rehabilitation, 98 (17.1%) patients did not have statin. They stated that they had never used statins before or that they stopped using them shortly after the event. This subgroup had significantly unfavorable values of lipid parameters (p<0.001), abdominal obesity (p<0.01), physical inactivity (p<0.01), more comorbidities (p<0.001), more prescribed medications on daily level (p<0.05), lower education degree level (p<0.01) and lower monthly income (p<0.001). Independent factors for not taking statin were: female gender, low monthly income and large number of comorbidities (R = 0.291, R2 = 0.85, adjusted R2 = 0.80, std. error of the estimate = 0.36151; p < 0.001). The patients themselves stated that the first reason for not taking statin was lack of financial funds (45.9%), while the second reason was normalization of laboratory results (21.4%). Three months after acute coronary event, 17.1% of patients in Serbia stopped taking statin. Lower adherence to statin closely correlates with female gender, low financial income and multiple comorbidities

Computing generalized inverses using LU factorization of matrix product

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse

Computation of generalized inverses using Php/MySql environment

The main aim of this paper is to develop a client/server-based model for computing the weighted Moore-Penrose inverse using the partitioning method as well as for storage of generated results. The web application is developed in the PHP/MySQL environment. The source code is open and free for testing by using a web browser. Influence of different matrix representations and storage systems on the computational time is investigated. The CPU time for searching the previously stored pseudo-inverses is compared with the CPU time spent for new computation of the same inverses.Comment: International Journal of Computer Mathematics, Volume 88, Issue 11, 201

Izračunavanje generalisanih inverza

Moj cilj nije bio da ispitujem implementaciju svih poznatih metoda za izračunavanje generalisanih metoda. Takođe mi nije bio cilj da poredim direktne i iterativne metode. Ja sam proučavao pojavu problema povećanje broja operacija u pokretnom zarezu, tokom iteracije, prouzrokovane ponovnim izračunaranjem pojedinih izraza, u numeričkim izračunavanjima pseudoinverza, kao i vezu proceduralnih i neproceduralnih programskih jezika i njihovu mogućnost u uzračunavanju generalisanih inverza. Predložio sam nove metode i nove algoritme, kao i modifikacije postojećih metoda i algoritama, koji rešavaju pomenute probleme. Sve je bazirano na mogućnostima paketa MATHEMATICA kao tipičnog primera programskog paketa za simboličko izračunavanje, i paketa DELPHI kao predstavnika proceduralnih programskih jezika. Metodi i algoritmi koje sam predložio implementirani su i testirani na numeričkim i racionalnim matricama, polinomijalnim matricama, retkoposednutim matricama i na bazama podataka. Oni su primenljivi na sve proceduralne programske jezike

Influence of running conditions on resonant oscillations in fresh-air ventilator blades used in thermal power plants

High frequency cyclic load of fresh air supply to ventilator blades in thermo energetic facilities can cause the occurrence of fretting in the pressed overlap of ventilator shaft and socket. These loads can be generated by the resonant oscillations of ventilator blades and thermal residual stress due to welding. To prevent running in resonant conditions, the manufacturer of the ventilator defined a procedure of adjusting blades natural frequency in the process of production, as well as period control during exploitation period. The numerical simulations and the accelerations measured and presented in this paper, enabling analysis of mass changes and rotation rate effects on resonant oscillations occurrence in fresh air ventilator

Thermal management evaluation of the complex electro-optical system

The thermal management of a complex electro-optical system aimed for outdoor application is challenging task due to the requirement of having an air-sealed enclosure, harsh working environment, and an additional thermal load generated by sunlight. It is essential to consider the effect of heating loads in the system components, as well as the internal temperature distribution, that can have influence on the system life expectancy, operational readiness and parameters, and possibility for catastrophic failure. The main objective of this paper is to analyze internal temperature distribution and evaluate its influence on system component operation capability. The electro-optical system simplified model was defined and related thermal balance simulation model based on Solid Works thermal analysis module was set and applied for temperature distribution calculation. Various outdoor environment scenarios were compared to evaluate system temperature distribution and evaluate its influence on system operation, reliability, and life time in application environment. This work was done during the design process as a part of the electro-optical system optimization. The results show that temperature distribution will not be cause for catastrophic failure and malfunction operation during operation in the expected environment

Determination of changes in organizational and management processes in the management system

Managing business organizations is a complex and dynamic process, aimed at effectively and efficiently directing limited resources. Based on that, the business success of the company is largely conditioned by the quality and ability of its management to create an adequate organizational structure that will respond to the challenges in the environment. In recent decades, there have been numerous and dramatic changes in the business environment, which lead to a comprehensive transformation of existing management processes and thus the dynamic development of theory and practice of modern management

Corrosion Behavior of the Cu24Zn5Al Alloy in Sodium Sulfate Solution in the Presence of 1-Phenyl-5-mercaptotetrazole

The results of this research on the electrochemical behavior of Cu24Zn5Al alloy in a 0.1 mol/dm3 sodium sulfate (Na2SO4) solution containing 1-phenyl-5-mercaptotetrazole (PMT) are presented in this paper. The influence of PMT concentration, chloride ion concentration, and pre-treatment were examined. The influence of pre-treatment was studied in terms of the effect of the immersion time of the electrode in the appropriate inhibitor solution. After selecting the optimal immersion time, its effect on the behavior of the Cu24Zn5Al alloy was tested in a 0.1 mol/dm3 solution of sodium sulfate in the presence of different concentrations of chloride ions. Research shown that with the increase of PMT concentration, the anodic current density around the corrosion potential decreases, indicating that PMT behaves as a corrosion inhibitor for Cu24Zn5Al alloy